The Collaborative International Dictionary of English v.0.48:

Keenness \Keen"ness\, n.
   The quality or state of being keen.
   [1913 Webster]

WordNet (r) 3.0 (2006):

keenness
    n 1: a quick and penetrating intelligence; "he argued with great
         acuteness"; "I admired the keenness of his mind" [syn:
         acuteness, acuity, sharpness, keenness]
    2: a positive feeling of wanting to push ahead with something
       [syn: eagerness, avidity, avidness, keenness]
    3: thinness of edge or fineness of point [syn: sharpness,
       keenness] [ant: bluntness, dullness]

Moby Thesaurus II by Grady Ward, 1.0:

165 Moby Thesaurus words for "keenness":
   absolute zero, acerbity, acidity, acidness, acidulousness,
   acridity, acrimony, acuity, acumen, acumination, acuteness,
   adroitness, agility, alacrity, alertness, algidity, animation,
   anxiety, anxiousness, appetite, aptitude, aptness, asperity,
   astringency, astuteness, attention, attentiveness, avidity,
   avidness, bite, bitingness, bitterness, bleakness, braininess,
   breathless impatience, brightness, brilliance, briskness,
   causticity, causticness, cheerful readiness, chill, chilliness,
   clear thinking, cleverness, cold, coldness, cool, coolness, coolth,
   corrosiveness, crispness, cryogenics, cryology, cuttingness,
   decrease in temperature, dexterity, discernment, discrimination,
   eagerness, edge, elan, esprit, facetiousness, fierceness, flair,
   forwardness, freezing point, freshness, frigidity, frostiness,
   funniness, gelidity, genius, giftedness, gifts, grip, gust, gusto,
   harshness, humorousness, iciness, impatience, incisiveness,
   inclemency, intense cold, jocoseness, jocularity, joking, joshing,
   keen desire, keen-wittedness, life, liveliness, low temperature,
   mental alertness, mercurial mind, mordacity, mordancy, mucronation,
   native cleverness, nimble mind, nimble-wittedness, nimbleness, nip,
   nippiness, nous, penetration, percipience, perspicacity,
   piercingness, piquancy, pleasantry, poignancy, point, pointedness,
   prickliness, promptitude, promptness, punctuality, pungency,
   quick parts, quick thinking, quick wit, quick-wittedness,
   quickness, rawness, readiness, ready wit, rigor, roughness,
   saltiness, savvy, severity, sharp air, sharp-wittedness, sharpness,
   shrewdness, sleeplessness, smartness, smarts, sourness, spinosity,
   spirit, sprightly wit, stabbingness, sting, stridency, stringency,
   talent, tartness, teeth, thorniness, trenchancy, vehemence, verve,
   violence, virulence, vitality, vivacity, wakefulness, wit,
   wittiness, zest, zestfulness